Applied geminography - symmetry analysis of twinned crystals and definition of twinning by reticular polyholohedry

The common classification of twinning into the four categories of twinning by merohedry ( complete and exact overlap of the lattices of the twinned crystals), pseudomerohedry ( complete but approximate overlap), reticular merohedry ( partial but exact overlap) and reticular pseudomerohedry ( partial and approximate overlap) is revised in terms of the complete ( translational and point) lattice symmetry of the twin and of the individual. The new category of reticular polyholohedry is introduced for twins where the twin lattice has the same point symmetry but a different orientation of the individual lattice. It is shown that the degeneration to twin index 1 relates, in a parallel way, reticular merohedry to metric merohedry and reticular polyholohedry to syngonic merohedry. Some examples from the recent literature are analysed in terms of this revised classification.